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Home » A takes 10 days less than the time taken by to finish a piece of work. If both and together can finish the work in 12 days, find the time taken by to finish the work.
A takes 10 days less than the time taken by \mathrm{B} to finish a piece of work. If both \mathrm{A} and \mathrm{B} together can finish the work in 12 days, find the time taken by \mathrm{B} to finish the work.
CBSE | Class 10 | Exercise 10e | Maths | Quadratic Equations | RS Aggarwal
A takes 10 days less than the time taken by \mathrm{B} to finish a piece of work. If both \mathrm{A} and \mathrm{B} together can finish the work in 12 days, find the time taken by \mathrm{B} to finish the work.

Let B takes x days to complete the work.

Therefore, A will take (x-10) days.

\begin{array}{l} \therefore \frac{1}{x}+\frac{1}{(x-10)}=\frac{1}{12} \\ \Rightarrow \frac{(x-10)+x}{x(x-10)}=\frac{1}{12} \\ \Rightarrow \frac{2 x-10}{x^{2}-10 x}=\frac{1}{12} \\ \Rightarrow x^{2}-10 x=12(2 x-10) \\ \Rightarrow x^{2}-10 x=24 x-120 \\ \Rightarrow x^{2}-34 x+120=0 \\ \Rightarrow x^{2}-(30+4) x+120=0 \\ \Rightarrow x^{2}-30 x-4 x+120=0 \\ \Rightarrow x(x-30)-4(x-30)=0 \\ \Rightarrow(x-30)(x-4)=0 \\ \Rightarrow x=30 \text { or } x=4 \end{array}

Number of days to complete the work by B cannot be less than that by \mathrm{A}; therefore, we get: x=30

Thus, B completes the work in 30 days.

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